Quant Quiz (Arithmetic) for SSC CGL Tier-II 2016

Q1. A man and a boy received Rs. 800 as wages for 5 days for the work they did together. The man’s efficiency in the work was three times that of the boy. What are the daily wages of the boy?
(a) Rs. 76
(b) Rs. 56
(c) Rs. 44
(d) Rs. 40
S1. Ans.(d)
Sol. Wages of a worker directly proportional to their efficiency when they work together for a same period of time efficiency of man and woman = 3 : 1
Ratio of wages = 3 : 1
So, wage of boy for a 5 days = 800/4 = 200
For one day = 200/5 = 40 Rs.

Q2. A can cultivate 2/5 of a land in 6 days and B can cultivate 1/3 of the same land in 10 days. Working together, A and B can cultivate 4/5 of the land in:
(a) 4 days
(b) 5 days
(c) 8 days
(d) 10 days
S2. Ans.(c)
Sol. A can cultivate full part of land = 6×5/2=15 days
B can cultivate full part of the land = 10×3=30 days
Let A and B both take x days to cultivate 4/5 of the land
According to question,
x[1/15+1/30]=4/5
x=8 days

Q3. Work done by A in one day is half of the work done by B in one day. Work done by B is half of the work done by C in one day. If C alone can complete the work in 7 days, in how many days can A, B and C together complete the work?
(a) 28
(b) 14
(c) 4
(d) 21
S3. Ans.(c)
Sol. Suppose, A does a work in x days.
B does similar work in x/2 days and C does in x/4 days.
∵x/4=7/1
⇒x=4×7
x=28
∵1/28+1/14+1/7=(1+2+4)/28
=7/28=1/4
So,A, B and C together complete the work in 4 days


Q4. 2 men alone or three women alone can complete a piece of work in 4 days. In how many days can 1 woman and one man together complete the same piece of work?
(a) 6 days
(b) 24/5 days
(c) 12/1.75 days
(d) Cannot be determined
S4. Ans.(b)
Sol. 2 men = 2 women
1 man + 1 woman = (3/2+1) women = 5/2 women
∵ M1 D1=M2 D2
⇒3×4=5/2×D2
∴D2=(3×4×2)/5=24/5  days

Q5. Jaydeep purchased 25 kg of rice at the rate of Rs. 16.80 per kg and 35 kg of rice at the rate of Rs. 25.50 per kg. He mixed the two and sold the mixture. Approximately, at what price per kg did he sell the mixture to make 25 per cent profit?
(a) Rs. 26.50
(b) Rs. 27.50
(c) Rs. 28.50
(d) Rs. 30.00

Q6. The ratio between the ages of a father and a son at present is 5 : 2, 4 years, hence the ratio between the ages of the son and his mother will be 1 : 2. What is the ratio between the present ages of the father and the mother?
(a) 3 : 4
(b) 5 : 4
(c) 4 : 3
(d) Cannot be determined
S6. Ans.(d)
Sol. Let, the ages of father and son are 5x and 2x years.
After four years the age of son = 2x+4
After four years the age of mother = 4x+8
So the present age of mother = 4x+4
Ratio of the age of father and mother = 5x∶(4x+4)
Data are insufficient, so cannot be determined.

Q7. The sum of the ages of 4 members of a family, 5 years ago, was 94 years. Today, when the daughter has been married off and replaced by a daughter-in-law, the sum of their ages is 92. Assuming that there has been no other change in the family structure and all the people are alive, what is the difference between the age of the daughter and that of the daughter-in-law?
(a) 22 years
(b) 11 years
(c) 25 years
(d) 19 years
S7. Ans.(a)
Sol. There are four members in a family. Five years ago the sum of ages of the family members = 94 years
Now, sum of present ages of family members = 94+5×4=114 years
∴ Daughter is replaced by daughter-in-law
Thus, sum of family member’s ages becomes 92 years.
∴ Difference = 114-92=22 years

Q8. A person borrows Rs. 5000 for two years at 4% per annum simple interest. He immediately lends to another person at 6 1/4% per annum for 2 years. Find his gain in the transaction per year:
(a) Rs. 112.50
(b) Rs. 450.00
(c) Rs. 244.53
(d) Rs. 150.00
S8. Ans.(a)
Sol. Difference in the rate of interest = 25/4-4
=9/4%
Gain in transaction per year = (5000× 9/4   × 1 )/100
= 112.50 Rs.

Q9. Nikhil invested certain amount in three different schemes A, B and C with the rate of interest 10% per annum, 12% per annum and 15% per annum, respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B?
(a) Rs. 8000
(b) Rs. 5000
(c) Rs. 6500
(d) Cannot be determined

S9. Ans.(b)

Sol. Ratio of investment in difference scheme = 100 : (150 × 100)/240 ∶150 

= 8 : 5 : 12
= 8x∶5x∶12x
 Now, according to question
(8x×10)/100+(5x×12)/100+(12x×15)/100=3200
 x=1000 
Amount invested in scheme B = 5×1000
= 5000 Rs. 
Q10. The simple interest accrued on a certain principal is Rs. 2000 in five years at the rate of 4 percent p.a. What would be the compound interest accrued on the same principal at the same rate in two years?
(a) Rs. 716
(b) Rs. 724
(c) Rs. 824
(d) Rs. 816

Q11. In an election there were only two candidates. One of the candidates secured 40% of votes and is defeated by the other candidate by 298 votes. The total number of votes polled is :
(a) 745
(b) 1460
(c) 1490
(d) 1500
S11. Ans.(c)
Sol. Let the total number of votes polled be x
Now, according to the question,
x((60-40)/100)=298
⇒x×1/5=298
⇒x=298×5=1490

Q12. A jar contains 10 red marbles and 30 green ones. How many red marbles must be added to the jar so that 60% of the marbles will be red ?
(a) 25
(b) 30
(c) 35
(d) 40
S12. Ans.(c)
Sol. Let the red marbles be added be x.
Now, according to the question,
(10+x)/(40+x)×100=60
⇒  ((10+x)×5)/(40+x)=3
⇒50+5x=120+3x
⇒5x-3x=120-50
⇒2x=70 ⇒x=70/2=35

Q13. Mr X invested a certain amount in Debt and Equity Funds in the ratio of 4 : 5. At the end of one year, he earned a total dividend of 30% on his investment. After one year, he reinvested the amount including the dividend in the ratio of 6 : 7 in Debt and Equity Funds. If the amount reinvested in Equity Funds was Rs. 94,500, what was the original amount invested in Equity Funds ?
(a) Rs. 75,000
(b) Rs. 81,000
(c) Rs. 60,000
(d) Rs. 65,000
S13. Ans.(a)
Sol. Amount reinvested in equity funds = 94500
Amount reinvested in debt + equity funds
=94500×13/7=175500
Amount invested earlier in debt + equity funds
=175500/1.3=135000
Original amount invested in equity funds
=5/9×135000=75000

Q14. The product of one-third of a number and 150% of another number is what per cent of the product of the original numbers ?
(a) 80%
(b) 50%
(c) 75%
(d) 120%
S14. Ans.(b)
Sol. Let the original numbers be x and y and their product be xy.
Product of 1/3rd of x and 150% of y=x/3×3/2 y=xy/2
Required answer = xy/(2 × xy)×100=50%

Q15. A, B and C working individually can complete a piece of work in 10, 15 and 20 days respectively. They completed the work in 4 days with the help of D. If they earned Rs. 3750 for the entire work, how much did D earn for work?
(a) Rs. 450
(b) Rs. 500
(c) Rs. 550
(d) Rs. 600 

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